ch 9 Flashcards
Annuity: a stream or series of equal payments to be received in the future.
Annuity: a stream or series of equal payments to be received in the future.
The payments are assumed to be received at the end of each period (unless stated otherwise).
A good example of an annuity is a lease, where a fixed monthly charge is paid over a number of years.
What will be the future value of $1,000 to be received at the end of each year for 4 years given a 10% interest rate?
PV= 0 PMT = -1000 I/Y= 10% N=4 FV=? 4641
What will be the future value of $1,000 to be received at the
beginning of each year for 4 years given a 10% interest rate?
pv=?= 3486.85 FV= 0 PMT= -1000 N= 4 I/Y=10 BGN KEY ON
Assuming we wish to accumulate $4,641 after four years at a 10% interest rate, how much do we need to set aside at the end of each of the four periods?
PV= 0 FV = -4641 PMT=?=1000 I/Y =10 N=4
A $10,000 investment will generate $1,490 a year for the next 10 years, what is the interest rate or yield on the investment?
PV= -1000 FV= 1464.10 PMT =0 N=4 I/Y= ? =10%
A problem may involve a combination of single amounts and an annuity. It is referred as a deferred annuity
Example:
What is the PV of an Annuity of $1,000 that will be paid at the end of each year from the fourth through the eight year, with a discount rate of 8 percent?
First, find the PV of the annuity of $1,000 being paid for 5 years beginning 4 years in the future with a discount rate of 8%
Next, find the PV of $3,992.71 to be received at the end of year 3 discounted back to the present with a discount rate of 8%
PV= ?= 3992.71 FV=0 N=5 I/Y=8 PMT=1000
PV= ? = 3169.54 FV= 3992.71 PMT= 0 I/Y =8 N=3
The formula for a perpetual annuity (with equal payments at the end of the period) is as follows:
PV= A = PMT
__ ____
i i
The formula for a perpetual annuity growing at a constant rate (g) is as follows:
PV= A
___
i - g
The formula for an annuity growing at a constant rate (g) for a limited period of time (n) is as follows:
It is common to have mortgages that have interest compounded semiannually, with payments made monthly.
Calculations of the monthly payment must acknowledge the early payment of interest.
A 20-year, $80,000 mortgage carries an annual interest rate of 8% compounded semiannually. How much is the monthly payment?
First, we calculate the monthly effective interest
Next, we calculate the monthly payment on the mortgage using the monthly effective interest rate
fv= 1.04 pv= -1.0 n=6 pmt =0 i=?= 0.6558% press 6 2nd EFF 4 = 3.9349
PV= -80000 FV= 0 N= 240 (20 YRS X12) I/Y= .6558 CPT PMT = 662.69
The financial manager uses the time value of money approach to value cash flows that occur at different points in time.
A dollar invested today at compound interest will grow to a larger value in future. That future value, discounted at compound interest, is equated to a present value today.
Cash payments may be received for an infinite period (perpetuity) in equal payments, or with payments growing at a constant rate.
A financial asset (security) is a claim against a firm, government or individual for future expected cash flows.
what are some examples
Examples of financial assets are bonds, preferred stocks and common stocks.
An investment decision should be made by:
comparing the price (or market value) of a financial asset to its present value.
determining the discount rate that equates the market value of a financial asset with the present value of its future expected cash flows.
This discount rate is the market-determined required rate of return (ROR) or yield.
The Required Real Rate of Return:
represents the opportunity cost of the investment
in the early 1990’s, 5-7%, but now about 2 to 3%
Inflation Premium:
a premium to compensate for the effects of inflation
Since 2000 slightly less than 2%
Risk Premium:
a premium associated with business and financial risk
default, liquidity and maturity risk
typically, 2-6%
The Required Rate of Return equals:
Real Rate of Return + Inflation Premium + Risk Premium
A bond contractually promises:
a stream of annuity payments, “I” (called interest or coupon)
And a final payment, Pn (called maturity, face or par value, usually is $1,000)
Find the price of a bond that pays 10% interest (coupon rate) when the required rate of return (current yield) is 12%, and the bond has 20 years remaining to maturity and a face value of $1,000
Using a calculator:
PV= ? =-850.61 FV= 1000 N= 20 I/Y= 12 PMT= 100
What the price of a $1,000 bond that pays a $100 interest payments for 20 periods and the required yield to maturity is 10%?
PV=?=-1000 FV=1000 PMT=100 N=20 I/Y=10
Bond prices are inversely related to bond yields
If Yields decrease, the Price of Bonds increase
If Yields increase, the Price of Bonds decrease
Determining the Required Rate of Return (Yield) from the Market Price:
Kp=Dp/Pp
- No Growth in Dividends
similar to preferred stock
Po=Do/Ke
- No Growth in Dividends
similar to preferred stock
Po=Do/Ke
- Constant Growth in Dividends
the dividend growth rate, “g”, must be constant forever.
the required rate of return, Ke, must exceed the growth rate, “g”
Po=D1/(Ke-g)
The required rate of return, Ke can be estimated
Using the Capital Asset Pricing Model (CAPM) (examined in Appendix 11A)
Or by using the current yield for long-term Government of Canada bond and a risk premium based on the level of risk of the common shares
The growth rate “g” is best estimated from the historical growth rate in dividends projected in the future
or “g” can be estimated from the growth in EPS, revenues per share, or cash flow per share if one or the other of these items are not available.
The Required Rate of Return consists of 2 things:
dividend yield = D1/P0
anticipated growth in the future = g
Ke=D1/Po +g
The Price-Earnings (P/E) ratio represents a multiplier applied to current earnings to determine the value of a share of stock in the market.
The P/E ratio is influenced by:
the earnings and sales growth of the firm the risk (or volatility in performance) the debt-equity structure of the firm the dividend policy the quality of management a number of other factors
A stock with a high P/E ratio:
indicates positive expectations for the future of the company
means the stock is more expensive relative to earnings
typically represents a successful and fast-growing company
is called a growth stock
A stock with a low P/E ratio:
indicates negative expectations for the future of the company
may suggest that the stock is a better value or buy
is called a value stock
When the firm experiences very rapid growth it is called _______ growth
supernormal
